Capacitive structures are used in MEM systems (micro electromechanical systems) to drive micro-mirrors, micro-structured circuits and sensors by means of electrostatic force.
A typical example for a sensor that uses capacitive structures both for compensation of forces as well as for actuation is the angular rate sensor. Known angular rate sensors are used in driver assistance systems, driving safety systems such as an electronic stability program, navigation systems and increasingly also in mobile devices such as mobile phones, tablet computers and game consoles. These known angular rate sensors thereby detect angular rates around a defined axis based on the coriolis effect.
Known angular rate sensors generally include, for example, two masses, including a primary and a secondary mass. To be able to detect an angular rate by means of the coriolis effect, the total mass has to be set in motion. The primary mass, in which the secondary mass is suspended, is oscillated constantly through electrostatic actuation with a constant frequency.
Through a rotation of the sensor around its sensitive axis, the secondary mass is deflected orthogonally to the primary axis in accordance with the following equation:Equation (1):{right arrow over (F)}c=−2·m·{right arrow over (Ω)}×{right arrow over (v)}p  (1)
Thereby, Fe is the coriolis force, m the mass, Ω the angular rate and vp the speed of the primary mass.
The secondary mass is thereby mechanically suspended in a way that it can only deflect orthogonally to the primary oscillation. To achieve a high linearity, large bandwidths and a reduced sensitivity in relation to process variations, these sensors are operated in a fed-back way.
Thereby, the effective coriolis force Fc is compensated by the application of a resetting capacitive force Fes to the secondary mass according to the following equation:Equation (2):{right arrow over (F)}C={right arrow over (F)}es  (2)
The application of this compensation signal, that counteracts the input variable, is called force feedback.
Hence, the secondary mass remains in the resting position and the generated capacitive force Fes is a direct measure for the angular rate that impacts on the system. To generate forces that are sufficiently high for the activation of the primary and the secondary mass, it is necessary to use electric voltages that are multiple times higher than typical supply voltages of integrated circuits. In addition, these high voltages are used to adjust the spring constant and, therefore, the resonance frequency of the secondary mass.
There is an attractive electrostatic force between two or several electrical electrodes with opposite charges (capacitance). This force can be quantitatively determined based on the change of the energy E stored in the capacitance with the distance between the electrodes x.
In case of parallel electrodes as they are used on the secondary side of angular rate sensors, the force Fes,p is calculated according to equation (3).
Equation (3):
                                          F            →                                es            ,            p                          =                                            ⅆ              E                                      ⅆ              x                                =                                    -                              1                2                                      ⁢                                                            ɛ                  0                                ⁢                                  ɛ                  r                                ⁢                A                                            x                2                                      ⁢                          V              2                                                          (        3        )            
Thereby, ∈r is the relative permittivity, ∈o the dielectric constant and V the voltage between the electrodes. A is the electrode surface (see FIG. 1a).
For the primary side, comb actuators are typically used in angular rate sensors in whose case the force Fes,k is calculated according to equation (4).
Equation (4):
In equation (4), N is the number of combs, d the constant distance between the electrodes and h the horizontal expansion of the electrodes. Both electrode configurations are shown in FIG. 1.
                                          F            →                                es            ,            k                          =                                            ⅆ              E                                      ⅆ              x                                =                                    -              N                        ⁢                                                  ⁢                                                            ɛ                  0                                ⁢                                  ɛ                  r                                ⁢                h                            d                        ⁢                          V              2                                                          (        4        )            
The force Fes,p generated by parallel electrodes is, in contrast to the force Fes,k, dependent on comb actuators with the distance x. As, however, the movement of the mass is compensated in the case of the secondary side, this dependency can be neglected. In both cases (FIG. 1a and FIG. 1b), the force is a quadratic function of the voltage.
Since electrostatic forces always have an attractive effect, the primary mass is driven differentially in the case of angular rate sensors and the movement of the secondary mass is also compensated differentially. As shown in FIG. 2, the mass and therefore also the counter-electrodes of the capacitances CFB1,2 are set on a fixed potential V0 for this purpose.
A voltage with a fixed direct voltage part VDC and a variable voltage part VAC(t) is applied to the second electrode with the capacitances CFB1,2. Thereby, the voltage VAC(t) is generally a rectangular voltage with a phase shifted by 180 degrees between CFB1 and CFB2. This results, according to the following equation (5), in the overall force Fes, tot that impacts on the mass and that is linearly dependent on the voltages VDC and VAC(t).
Equation (5):
                                          F            →                                es            ,            tot                          =                                            F                              es                ⁢                                                                  ⁢                1                                      -                          F                              es                ⁢                                                                  ⁢                2                                              =                                    -              2                        ⁢                                          C                                                      FB                    ⁢                                                                                  ⁢                    1                                    ,                  2                                            x                        ⁢                                          V                                  A                  ⁢                                                                          ⁢                  C                                            ⁡                              (                t                )                                      ⁢                          (                                                V                                      D                    ⁢                                                                                  ⁢                    C                                                  -                                  V                  0                                            )                                                          (        5        )            
The required electrostatic force can on one hand be generated by means of a high voltage generator and high voltage amplifiers.
The voltages VDC and VAC(t) required for the generation of electrostatic capacitive forces according to equation (5), shown in FIG. 3, are usually applied to the capacitive structures of the sensor by means of operation amplifiers. Such a circuit system is described in greater detail for example in the article by Lasse Alltonen, Mikko Saukoski, Kari Halonen: “On-chip Digitally Tunable High Voltage Generator for Electrostatic Control of Micromechanical Devices”, IEEE 2006 Custom Integrated Circuits Conference (CICC), p. 583-586, and is also an object of the WO 2007/015218 A1.
The maximum output voltage of the operation amplifiers is limited by their supply voltage. To generate sufficiently high forces, it is therefore generally necessary to use high voltage operation amplifiers (HV-OPV) that work with voltages above the chip supply voltage VDD. For this reason, a high voltage generator generates a significantly higher voltage VDD_HV out of the voltage VDD and provides this voltage to the HV-OPV as a supply voltage. Thereby, the high voltage generator has to provide both the static current for the operation of the HV-OPV and the dynamic current to charge and/or discharge the capacitances CFB1 and CFB2 during the switching processes of the voltage VAC(t). The control units, that are provided with low voltage, supply the signal to be amplified by the HV-OPV with a factor k based on a clock with the desired amplitude VAC/k and the DC voltage VDC/k. Through the operation of the HV-OPV in feedback mode, the voltages VDC and VAC(t) can be accurately set.
Furthermore, the electrostatic force can also be generated by means of a high voltage generator in direct connection to capacitive structures for the actuation as known, for example, from the WO 2012/10541 A1.
This known solution for the generation of defined high voltages on capacitive structures is shown in FIG. 4. Thereby, no HV-OPV is used and the controlled input voltage of the high voltage generator VDD_HV is applied directly to the capacitances CFB1 and CFB2. The high voltage generator is readjusted through an analog control signal from a control unit (e.g. digital to analog convertor). In spite of this readjustment possibility, the high voltage VDD_HV in the static state is a static voltage VDC in this case. This is useful in the application described for the WO 2012/130541 A1, e.g. as no varying voltages VAC(t) are required for the squaring compensation of angular rate sensors.
The known solutions have significant disadvantages though. In case of the circuit according to FIG. 3, they consist on one hand of the enormous power demand of the HV-OPV and on the other hand of the stringent requirements and the power demand of the high voltage generator. The generation of the voltage VDD_HV by the high voltage generator is always prone to losses. In addition, this voltage must in most cases exceed the maximum applicable input voltage of the amplifiers due to the HV-OPV architecture. Moreover, the high dynamic currents during switching of the voltage VAC(t) at the capacitances complicate the constant control of the high voltage VDD_HV.
The standby current of the HV-OPV in case of the frequently used class A amplifiers is dependent on the steepness of the edges and the capacitances CFB1,2 to be driven. As a high edge steepness is needed for the angular rate sensors, and as there are even greater parasitic capacitances parallel to the capacitances CFB1,2, the standby current is considerable in the described system. Apart from that, the power demand of the HV-OPV increases linearly with the supply voltage VDD_HV and hence the circuit claims a substantial share of the overall power demand of the sensor reading system for the generation of power.
In case of the known circuit according to FIG. 4, a significant disadvantage consists in the fact that only static voltages VDC can be generated. To drive the primary mass and the compensation of the movement of the secondary mass, however, temporally varying voltages VAC(t) are essential. In order to still transfer such a signal VAC(t) to the high voltage range with the configuration from FIG. 4, the digital control signal would have to be temporally varied and the high voltage generator would have to track the voltage VDD_HV fast enough. This comes with stringent requirements for the dynamics of the high voltage generator and hence an increased power consumption. In addition, it is only possible to raise the voltage actively in case of a variety of high voltage generators. The reduction of the voltage, in turn, mostly occurs passively through the load current of the application. This condition further increases the complexity of the high voltage generation circuit.
In addition, the high voltage generators used are usually switching power supply devices where a ripple is always superimposed on its voltage as a function of the switching frequency. For high-resolution angular rate sensors, this ripple has to be kept very low in order to prevent additional interference signals from being coupled in the system. In case the high voltage generator and the sensor are directly connected, this is generally only possible through the application of very high switching frequencies. This entails a further increase of the power demand of such systems.